African-Americans, both enslaved and free had plenty to do with the American Revolution, many of those enslaved were offered Freedom in exchange for service by the British Army. Between 3,000 and 4,000 formerly enslaved fled to the British lines and joined up, becoming known as Black Loyalists under a document known as Lord Dunmore's Proclamation:
I do hereby further declare all indented Servants, Negroes, or others, (appertaining to Rebels,) free that are able and willing to bear Arms, they joining His Majesty's Troops as soon as may be, foe the more speedily reducing this Colony to a proper Sense of their Duty, to His Majesty's Crown and Dignity.
Within a month of Lord Dunmore's Proclamation, an "Ethiopian Regiment" had been formed of former slaves and these men quickly joined the standard British Army. At wars end, many of their names would be listed in the Book of Negroes, a fascinating and important document detailing their origins, names and families. Many of these Black Loyalists would end up in Nova Scotia, Sierra Leone, or the Caribbean.
On the other side of the coin, many African-Americans served for the Continental Army as well, though their numbers can be speculated on. They served in Regiments of their own as well as in integrated units in the Colonial Army. One Hessian Officer remarked “The Negro can take the field instead of his master; and, therefore, no regiment is seen in which there are not negroes in abundance, and among them are able-bodied, strong and brave fellows.”
The main book on this topic is The Forgotten Fifth by Gary Nash, an excellent work by an excellent historian. This website also has a fantastic assortment of primary and secondary sources for you to understand the context and role of Black Loyalists better.
You have other answers about the actual role of slaves in the American Revolution (they fought for both the Americans and the British).
I am going to look at the symbolic role of slaves in the American Revolution, through the lens of the oil Painting, “The Death of Major Peirson”.
http://i.imgur.com/lVTjJLt.jpg
The subject of this painting, is far removed from the main battles of the American Revolution. It depicts the repulse of the French attack on the Channel Isle of Jersey, “the Battle of Jersey”, in which a French surprise attack on the Island was defeated by soldiers under the command of Major Peirson, who was killed in the action.
The painting depicts Peirson’s servant, a black, “Pompey”, shooting and killing the French Marksman who has just killed the major.
Pompey is shown dressed in the uniform of the “Royal Ethiopian Regiment”, a unit raised in North America from escaped slaves to fight for Britain. This uniform would certainly not have been worn in reality during the Battle of Jersey
The artist was John Singleton Copely, a Massachusetts loyalist.
I think the whole painting is a comment on the hypocrisy of the Revolutionaries proclaiming freedom, while tolerating slavery.
The black soldier depicted in the Painting is meant to represent Major Peirson's servant "Pompey" avenging the Major's death by shooting the French sniper who had just mortally wounded him.
Whether Major Peirson actually had a black servant named Pompey, and, if he did, whether he was even at the battle, let alone shooting Frenchmen, is dubious.
The uniform which Pompey is depicted as wearing is that of Lord Dunmore's "Royal Ethiopian" regiment. The Royal Ethiopian Regiment did exist. It was raised by Lord Dunmore from escaped slaves during the American revolution to fight against the Americans. The Royal Ethiopian Regiment fought in America, and reportedly had "Liberty to Slaves" embroidered on their uniforms.
Source: http://www.johnhorse.com/trail/00/bg/20.htm
The artist was John Singleton Copley, a Massachusetts loyalist. An inspiration for his painting was the famous painting "The Death of General Wolfe" by another American artist, Benjamin West, depicting Wolfe's death at the battle of the Plains of Abraham outside the walls of Quebec in the French and Indian War. West had also inserted a representative African American into his work of art. (Two in fact, though not nearly so prominently. See if you can spot them):
http://www.kenney-mencher.com/pic_old/18th_century/west_death_of_general_wolfe_1771.jpg
Copley was presumably inspired by that, but perhaps also by a belief that the American Revolution was hypocritical in proclaiming liberty while supporting slavery, and wishing to honor African Americans and the Royal Ethiopian Regiment in his art.
Source: http://atlanticportal.hil.unb.ca/acva/blackloyalists/en/context/gallery/copley.html
The subject of the painting was the Battle of Jersey. When French forces during the American Revolution invaded the Channel Island of Jersey, they surprised the Governor of the Island in his bed and forced him to sign a surrender. Major Peirson, the 24 year old commander of the garrison, refused to surrender and led the garrison and the Jersey militia in a counter attack against the French. He was killed earlier in the battle than at the final charge which defeated the French (which is where he is shown dying in the painting).
Even if the presence of Pompey at the battle is not attested by any contemporary sources (and if he was, he would not have been wearing the uniform of the Royal Ethiopian Regiment), there actually was a non-European at the battle.
The co-commander of the French invasion forces was Mir Sayyad, an Indian (from India, not from North America) general, serving in the French forces after having lost his lands to the British in India.